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Interval Branch-and-Bound algorithms for optimization and constraint satisfaction: a survey and prospects

Author

Listed:
  • Ignacio Araya

    (Pontificia Universidad Católica de Valparaíso)

  • Victor Reyes

    (Universidad Técnica Federico Santa María)

Abstract

Interval Branch and Bound algorithms are used to solve rigorously continuous constraint satisfaction and constrained global optimization problems. In this paper, we explain the basic principles behind interval Branch and Bound algorithms. We detail the main components and describe issues that should be considered to improve the efficiency of the algorithms.

Suggested Citation

  • Ignacio Araya & Victor Reyes, 2016. "Interval Branch-and-Bound algorithms for optimization and constraint satisfaction: a survey and prospects," Journal of Global Optimization, Springer, vol. 65(4), pages 837-866, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0390-4
    DOI: 10.1007/s10898-015-0390-4
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    References listed on IDEAS

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    1. Frédéric Messine, 2005. "A Deterministic Global Optimization Algorithm for Design Problems," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 267-294, Springer.
    2. Ignacio Araya & Gilles Trombettoni & Bertrand Neveu & Gilles Chabert, 2014. "Upper bounding in inner regions for global optimization under inequality constraints," Journal of Global Optimization, Springer, vol. 60(2), pages 145-164, October.
    3. Mihály Markót & Hermann Schichl, 2014. "Bound constrained interval global optimization in the COCONUT Environment," Journal of Global Optimization, Springer, vol. 60(4), pages 751-776, December.
    4. Ralph Kearfott, 2014. "On rigorous upper bounds to a global optimum," Journal of Global Optimization, Springer, vol. 59(2), pages 459-476, July.
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    Citations

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    Cited by:

    1. Ioannis A. Nikas & Vasileios P. Georgopoulos & Vasileios C. Loukopoulos, 2025. "Selective Multistart Optimization Based on Adaptive Latin Hypercube Sampling and Interval Enclosures," Mathematics, MDPI, vol. 13(11), pages 1-29, May.
    2. Li, Yan & Zhang, Peng & Yue, Meng, 2018. "Networked microgrid stability through distributed formal analysis," Applied Energy, Elsevier, vol. 228(C), pages 279-288.
    3. Victor Reyes & Ignacio Araya, 2021. "AbsTaylor: upper bounding with inner regions in nonlinear continuous global optimization problems," Journal of Global Optimization, Springer, vol. 79(2), pages 413-429, February.
    4. N. Kazazakis & C. S. Adjiman, 2018. "Arbitrarily tight $$\alpha $$ α BB underestimators of general non-linear functions over sub-optimal domains," Journal of Global Optimization, Springer, vol. 71(4), pages 815-844, August.
    5. Ignacio Araya & Victor Reyes, 2019. "Enhancing interval constraint propagation by identifying and filtering n-ary subsystems," Journal of Global Optimization, Springer, vol. 74(1), pages 1-20, May.
    6. Ignacio Araya & Victor Reyes, 2025. "A revised monotonicity-based method for computing tight image enclosures of functions," Journal of Global Optimization, Springer, vol. 91(2), pages 257-286, February.
    7. Victor Reyes & Ignacio Araya, 2023. "Non-Convex Optimization: Using Preconditioning Matrices for Optimally Improving Variable Bounds in Linear Relaxations," Mathematics, MDPI, vol. 11(16), pages 1-19, August.

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